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I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least 800 pounds more than each of her trucks, but no more than \(\frac{1}{5}\) of the total load her four trucks combined can carry. Based on these facts, what is the greatest load I can be sure that my large truck can carry, in pounds?

 Jan 18, 2022
 #1
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The answer is 1200 pounds.

 Jan 18, 2022
 #2
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We have two conditions 

Let x = the load of your teuck

and y = load of their trucks then

1)  x ≥ y + 800 .... (1)

   4y = the total load of their trucks

(1/5) * 4y = the load of your truck

2)   4/5 * ≤ y .... (2)

Calculations:-

                       x = y + 800 .... (1)

                       x = 5y/4 .... (2)

Put value of (2) in (1) so

              5y/4 = y + 800

         => 5y/4y - y = 800

         => 1/4y = 800

         =>  y = 3200 pounds

then put y = 3200 in (2)

       x = 5/4 (3200)

       x = 4000 pounds

4000 pounds is the greatest load that your truck carry

 Jan 20, 2022

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